Final answer:
Most new membrane synthesis in a eukaryotic cell takes place in the endoplasmic reticulum, specifically in the rough endoplasmic reticulum (RER) where protein synthesis occurs on ribosomes. The Golgi apparatus then modifies these proteins and lipids before they are distributed.
Step-by-step explanation:
The majority of new membrane synthesis in a eukaryotic cell takes place in the endoplasmic reticulum. The endoplasmic reticulum (ER) is a network of interconnected tubules and sacs that spans throughout the cytoplasm of the cell. It is involved in various cellular functions, including the synthesis of lipids and proteins.
The endoplasmic reticulum can be classified into two types: rough endoplasmic reticulum (RER) and smooth endoplasmic reticulum (SER). The RER is studded with ribosomes on its surface, where protein synthesis occurs. These ribosomes synthesize proteins that are destined to be inserted in the cell membrane or exported outside the cell. Therefore, most new membrane synthesis, including the synthesis of proteins that make up the membrane, happens in the RER.
The Golgi apparatus, another organelle in the cell, further modifies these newly synthesized proteins and lipids before they are distributed to their final destinations.